Calculate the net electric field due to a rod of linear charge density \(\lambda= 5\mu\,\text{C/m}\) on a point lying on a perpendicular bisector at distance R = 3 m and making an angle \(\theta=\) 37° between perpendicular bisector and on end of rod.

A

6 × 103 N/C

.

B

18 × 103 N/C

C

5 × 103 N/C

D

4 × 107 N/C

Option B is Correct

Calculation of Electric Field at a Point due to Combination of Section of Ring and Rod

Consider a section of ring of radius R as shown in figure.

To calculate electric field at the center of ring due to section of ring, choose the element on the ring.

An element of length \(d\ell\) subtending an angle \(d\alpha\) at the center of the ring, as shown in figure.

The horizontal components of electric field will cancel out and vertical component will get added, as shown in figure.